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Made available in DSpace on 2015-05-14T12:14:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 735779 bytes, checksum: 2ffa25e5b45beedc0c8f4f31d5f79b06 (MD5) Previous issue date: 2013-06-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we review some basic concepts related to Lorentz symmetry violation and Horava-Lifshitz-like theories. We present our contribution to the calculation of the effective potential in two frameworks that exhibit Lorentz invariance violation. First, we calculate the effective potential for some HL-like theories. We obtained results for the pure scalar model, for the scalar QED with critical exponent z = 2 and z generic, and for the Yukawa model also with z = 2 and with arbitrary values of z. For the latter model, we show that the effective potential vanishes for even z and has nontrivial values for odd z. The second framework is the Kostelecký-Berger model that implements the Lorentz symmetry breaking in supersymmetry. We develop the theory of superfields for three and four-dimensional space-time based on this model and show how this development leads to a theory of superfields with ether-like Lorentz violation. We also obtained the one loop contributions to the effective action and effective potential in this theory. / Nesta tese, revisamos alguns conceitos básicos relacionados à violação da simetria de Lorentz e a teorias do tipo Horava-Lifshitz. Apresentamos nossa contribuição ao cálculo do potencial efetivo em duas formulações que exibem violação da invariância de Lorentz. Primeiro, calculamos o potencial efetivo para algumas teorias do tipo HL. Obtivemos resultados para o modelo escalar puro, para a QED escalar com expoente crítico z = 2 e z genérico, e para o modelo de Yukawa também com z = 2 e com valores arbitrários de z. Para este último modelo, demonstramos que o potencial efetivo se anula para z par e possui valores não triviais para z ímpar. A segunda formulação é o modelo de Kostelecký-Berger que implementa a quebra da simetria de Lorentz em supersimetria. Desenvolvemos a teoria de supercampos para três e quatro dimensões do espaço-tempo com base neste modelo e mostramos como este desenvolvimento leva a uma teoria de supercampos com violação de Lorentz do tipo-éter. Obtemos também as contribuições de um loop para a ação efetiva e para potencial efetivo nesta teoria.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T12:27:38Z No. of bitstreams: 1 arquivototal.pdf: 987629 bytes, checksum: 073f4a58e014f0b46588edf144d4a42b (MD5) / Made available in DSpace on 2017-09-12T12:27:38Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 987629 bytes, checksum: 073f4a58e014f0b46588edf144d4a42b (MD5) Previous issue date: 2016-02-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation we work with the Horava-Lifshitz-like Gross-Neveu model in (2+1) dimensions in the Large N expansion. Firstly we make an article revision [6] where it is shown that the Gross-Neveu Model in the 1/N expansion presents a dynamic mass generation by means of the introduction of an auxiliary field, which results in the dynamical parity broken. We calculate the gap equation where we will see the generated mass dependence with the coupling constant. After that, we will put a gauge field to the model and study the polarization tensor which will generate an induced Chern-Simons term in the Effective Lagrangian. As a novelty, we work with the Gross-Neveu Model in the context of Horava-Lifshitz, where anisotropic scaling is done, thus breaking the Lorentz invariance. We introduce an auxiliary field and we study the cases which the value of the critical dynamic exponent Z is even and when it is odd. In the case where z is even, there is no dynamic mass generation so the parity symmetry is conserved and we will not have the term induced of Chern-Simons either. In the case where z is odd, we will have the dynamic mass generation and the dynamic parity symmetry will occur. Finally we couple a gauge field in the model and find the Chern-Simons term, which clearly shows the anisotropy of space and time for values of z> 1 / Nesta dissertacao trabalhamos corn o modelo de Gross-Neveu ern (2+1) dimensoes na expansao 1/N no contexto de Horava-Lifshitz. Primeiro, faremos uma revisao do artigo [6], onde se mostra que o Modelo de Gross-Neveu na expansao 1/N apresenta uma geracao dinamica de massa mediante a introducao de urn campo auxiliar, o que traz como consequencia a quebra dinamica da simetria de paridade. Calculamos a equacao de gap, onde veremos a dependencia da massa gerada corn a constante de acoplamento. ApOs isso, acoplaremos urn campo de gauge ao modelo, estudamos o tensor de polarizacao, o qual vai gerar urn termo induzido de tipo Chern-Simons na lagrangiana efetiva. Como novidade, trabalhamos corn o Modelo de Gross-Neveu no contexto de Horava-Lifshitz, onde se faz urn escalonamento anisotrOpico, quebrando, assim, a invariancia de Lorentz. Introduzimos urn campo auxiliar e estudamos os casos ern que o valor do exponente dinamico critico z é par quando é Impar. No caso ern que z é par, nao ha geracao dinamica de massa pelo que a simetria de paridade é conservada e tambern nao teremos o termo induzido de Chern-Simons. No caso ern que z é impar, vamos ter a geracao dinamica de massa vai ocorrer a quebra dinamica de simetria de paridade. Finalmente, acoplamos urn campo de gauge no modelo e encontramos o termo tipo Chern-Simons, o qual mostra claramente a anisotropia do espaco tempo para valores de z > 1.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-17T19:12:16Z No. of bitstreams: 1 KLECIO EMANUEL LIMA DE FARIAS – DISSERTAÇÃO (PPGFísica) 2017.pdf: 669446 bytes, checksum: 26edbf33fb48c30aed37e5d2c6da2a80 (MD5) / Made available in DSpace on 2018-10-17T19:12:16Z (GMT). No. of bitstreams: 1 KLECIO EMANUEL LIMA DE FARIAS – DISSERTAÇÃO (PPGFísica) 2017.pdf: 669446 bytes, checksum: 26edbf33fb48c30aed37e5d2c6da2a80 (MD5) Previous issue date: 2017-10-04 / Capes / Neste trabalho, aplicamos o reescalonamento tipo ao de Hoˇrava-Lifshitz para reescrever algumas teorias eletrodinâmicas de altas ordens derivativas que violam a simetria de Lorentz, controladas por quadrivetores: (n )s que determinam direções preferenciais no espaço - tempo. As equações de movimento foram obtidas, através das quais analisamos as relações de dispersão modificadas em conjunto com os resultados observacionais das experiências de explosão de raios gama (GRB). Os limites do expoente crítico foram discutidos a partir dos dados dos GRBs através de cálculos de grau de polarizaçao (usando operador de dimensão-cinco) e de atraso temporal (usando operador de dimensão-seis) nas propagações dos fótons. As implicações físicas foram comparadas com recentes resultados da literatura sobre limites da quebra da invariância de Lorentz via GRBs. / In this work, we used a Hoˇrava-Lifshitz scaling to rewrite a high-order derivative electrodynamics that violates the Lorentz symmetry, controlled by 4-vector (n )s which determine the space-time preferential directions. The equations of motion were obtained, through which the modified dispersion relation was analyzed together with observational results of gamma ray bursts (GRB). The limits of the critical exponent were discussed from the GRBs values through calculation of degree of polarization (using five-dimensional operator) and temporal delay (using six-dimensional operator) on photon propagation. The physical implications were compared with the current results from the literature regarding Lorentz invariance violation via GRB.

In dieser Doktorarbeit werden wir das Renormierungsproblem von Gravitationstheorien im Kontext der Renormierungsgruppe (RG) unter Anwendung von perturbativen und nicht-perturbativen Methoden untersuchen. Insbesondere werden wir uns auf verschiedene Gravitationsmodelle und Näherungen konzentrieren, in welchen die zentrale Rolle von einem skalaren Freiheitsgrad eingenommen wird. Wir konzentrieren uns besonders auf zwei Ansätze für Quantengravitation, die in letzter Zeit viel Aufmerksamkeit erhalten haben, nämlich den asymptotisch sicheren Fall der Gravitation und die Hořava-Lifshitz Quantengravitation. Das Prinzip der Asymptotischen Sicherheit beruht auf der Annahme, dass das hochenergetische Gravitationsregime von einem nicht-Gaußschen Fixpunkt bestimmt wird, der nicht-perturbative Renormierung und Endlichkeit der Korrelationsfunktionen sicherstellt. Wir werden die Existenz eines solchen nicht-trivialen Fixpunktes mit Hilfe der funktionalen Renormierungsgruppe untersuchen. Insbesondere werden wir den einzigen konformen Freiheitsgrad quantisieren. Die Frage nach der Existenz eines nicht-Gaußschen Fixpunktes in einem unendlich- dimensionalen Parameterraum, das heißt für eine generische f(R)-Theorie, kann jedoch nicht mit einem solchen konform reduzierten Model analysiert werden. Deshalb werden wir es untersuchen, indem wir eine skalare dynamische Äquivalentstheorie, das heißt eine generische Brans-Dicke Theorie in der lokal-Potential Näherung mit ω = 0, quantisieren. Schließlich werden wir mittels einer perturbativen RG Methode die asymptotische Freiheit der Hořava-Lifshitz Gravitationstheorie analysieren. Diese Gravitationstheorie beruht auf der Entstehung einer Anisotropie zwischen Raum und Zeit, die Newtons Konstante zu einer marginalen Koppelung werden lässt und explizit die Unitarität bewahrt. Insbesondere werden wir die Einschleifenkorrektur in 2+1 Dimensionen berechnen, indem wir nur den konformen Freiheitsgrad quantisieren. / In this Ph.D. thesis we will study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we will focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Hořava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We will then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson’s renormalization group. In particular we will quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we will study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω = 0 in the local potential approximation. Finally, we will investigate, using a perturbative RG scheme, the asymptotic freedom of the Hořava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton’s constant to a marginal coupling and explicitly preserves unitarity. In particular we will evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.